How To Add & Subtract Negative Fractions

Negative fractions are like any other fraction, except that they have a preceding negative (-) sign. The process of adding and subtracting negative fractions can be straightforward, if you keep in mind two things. A negative fraction added to another negative fraction will result in a negative fraction as result. A negative fraction subtracted from another is the same thing as adding the positive complement of that fraction.

Step 1

Make the denominators (the bottom of the fraction) the same, if they are not already. You can only add halves to halves or quarters to quarters or tenths to tenths and so on. Subtraction of negative fractions follows the same method.

Thus, if the negative fractions you are adding do not have the same denominator, you can make it so.

-1/2, for example, can be written as -2/4, -3/6, -4/8, et cetera. In each case, the number at the top is always half the number at the bottom. These fractions all mean half of a quantity.

Step 2

Consider the adding and subtracting of the following negative fractions.

- 1/4 + (-3/10) – 1/4 – (-3/10)

The first example is the addition of negative three-tenths to negative one-fourth. The second is the subtraction of negative three-tenths from negative one-fourth.

Step 3

Method: You cannot add one-fourths to three-tenths until you express both of them to a uniform standard, so that you have a common point of reference with which you can work. You can only add like to like, or subtract like from like. More like being able to compare apples to oranges only when you at least call them both pieces of fruit.

You need a common denominator. This will be the lowest number that the two denominators 4 and 10 will divide into. This will be 20.

Step 4

Keep the fraction equivalent using this common denominator: 20.

(- 1/4) becomes (- 5/20), because 5 is a quarter of 20.

(- 3/10) becomes (- 6/20). The denominator increased 2 times, so the numerator, the top part, has to double also, to keep the fraction the same.

Now that a common denominator has been found, and the negative fractions expressed in terms of this new denominator, the negative fractions can then be added or subtracted.

When adding negative fractions, add as per normal. Then stick the negative sign to your answer.

When subtracting negative fractions, you are, in effect, adding the positive complement of the negative fraction you are subtracting, because subtracting a negative number or fraction is the same as adding the positive of that negative fraction or number. The two consecutive negative signs "cancel out" to give a positive sign.

Step 5

Adding the negative fractions: (- 1/4) + (- 3/10) = – 5/20 + – 6/20 = – (11/20)

When subtracting: (- 1/4) – (- 3/10) = – 5/20 – (- 6/20) \= – 5/20 + 6/20 (two consecutive minus signs become a + sign) \= 1/20.